LTE-Advanced Transmit Diversity Decoders

ABSTRACT

Various embodiments of a transmit diversity decoding techniques are provided. In one aspect, a method receives a first input that includes signals transmitted by M transmit antennas on C channels and received by N receive antennas, where M, N and C is each a positive integer greater than 1. The method also receives a second input that includes estimates of channel matrix elements. The method further generates an output that includes at least an estimate of a transmit signal transmitted by one of the M transmit antennas on one of the C channels based at least in part on the first and the second inputs.

CROSS REFERENCE TO RELATED PATENT APPLICATION

This application is a continuation, and claims the priority benefit, ofU.S. patent application Ser. No. 13/467,865, filed May 9, 2012 andentitled “LTE-Advanced Transmit Diversity Decoders”, which is hereinincorporated by reference in its entirety.

BACKGROUND

1. Technical Field

The present disclosure relates to telecommunication and, morespecifically, to wireless communication transmit diversity decoding.

2. Description of Related Art

The new 4G wireless technology standard termed Long TermEvolution-Advanced (LTE-A) utilizes the well-known modulation schemeknown as orthogonal frequency division multiple access (OFDMA). It is amulticarrier technique in which the transmit spectrum is divided into Korthogonal subcarriers equally spaced in frequency. The method has beenused for many years in both wireline broadband communications andwireless local area networks (WLAN). LTE-A provides a minimum of 1000Mbps throughput in the downlink (DL) and 500 Mbps in the uplink (UL).The spectral bandwidth for LTE-A is 100 MHz, using up to five componentcarriers each with a component bandwidth of up to 20 MHz. LTE-A alsoincludes support for both frequency domain duplexing and time domainduplexing. LTE-A also employs multiple antenna methods such as spatialmultiplexing and transmit diversity. Spatial multiplexing (SM) is amultiple-input-multiple-output system (MIMO) formulation enabled byconfiguring multiple antennas separated in space. The spatiallyseparated antennas provide separate and distinct transmission channelsallowing the transmitter-receiver pair to extract independent signalsfrom each channel while cancelling interference from the othertransmission paths. When combined, OFDMA and MIMO-SM provideorthogonality in both frequency and space. LTE-A supports up to eightantennas per modem.

Another application of a MIMO system configuration is to providetransmit diversity. Transmit diversity, as the name implies, enables thetransmitter to send multiple copies of the same signal (or processedvariations of the same signal) over several of the separate antennapaths available when the transmitting and receiving modems have morethan one antenna. Wireless communications systems must contend withradio signal propagation impairments that include multipath fading,noise, and interference. Multipath fading results from a transmittedradio signal transversing many different paths from a transmittingantenna to a receiving antenna as a result of reflections from bothman-made and natural environmental objects. The multiple reflectedsignals (including a possible line-of-sight signal) combine at thereceiver to form a transmission path impulse response (with anassociated transmission path frequency response). Depending on thecharacteristics of this response, it is possible for parts of thetransmission channel to have deep nulls, which can be time-varying as aresult of movement of the transmitter, the receiver, and the objectscausing reflections. A wireless MIMO system has different transmissionpaths for its spatially separated antennas. The transmission pathdiversity increases the probability that the transmit signal can becorrectly received at the decoder while some of the transmission pathsare subject to harsh attenuation as a result of the multipath fadingproblem.

FIGS. 4-7 show some examples of MIMO system configuration. Morespecifically, FIG. 4 shows a single-input-single-output (SISO) system ina single cell for a single user between an LTE base station 410 and auser equipment 420. FIG. 5 shows a multiple input, single output (MISO)system in a single cell for a single user between an LTE base station510 and a user equipment 520. FIG. 6 shows a MIMO system in a singlecell for a single user between an LTE base station 610 and a userequipment 620. FIG. 7 shows a MIMO system, or interference, in acooperative multi-cell environment for a single user between LTE basestations 710, 715 and user equipment 720, 725.

The description below provides background information on MIMOcommunications for OFDM.

Optimal multi-antenna formulation for OFDM spatial multiplexing, wherethere are M antenna to transmit signals and N antennas to receivesignals, assumes that the duration of the time response of the channelis less than the OFDM cyclic prefix (CP), hence no inter-symbolinterference (ISI), and is expressed as follows:

r=Hy+n

where:

-   -   H=M×N MIMO channel frequency response matrix (M being the number        of transmit antennas, N being the number of receive antennas);    -   r=received frequency domain signal;    -   y=precoder frequency domain output signal;    -   n=noise; and    -   s=detected frequency domain signal.

If OFDM, the FFT (receiver demodulator) and IFFT (transmit modulator)provide transformation of signals between the time domain and frequencydomain. The MIMO channel formulation is used to model the channelresponse from the frequency domain signal in the transmitter to thefrequency domain signal in the receiver.

Channel diagonalization via the well-known singular value decomposition(SVD) can be expressed as follows:

H=SVD(H)=UDV ^(H)

where U, V are unitary eigenvector matrices and D is a diagonaleigenvalue matrix. Several well established methods and algorithms areavailable in text books and papers to calculate the SVD.

Further, with respect to the following expression:

r=UDV ^(H) y+n

it is assigned that y=Vx and s=U^(H)r as the (modified) transmit andreceive signals, respectively, where x is the precoder input signal.This provides the following:

S=U ^(H) r=U ^(H) UDV ^(H) Vx+U ^(H) n

s=Dx+U ^(H) n

Since D is diagonal, the antenna channels are now orthogonalized andspatial interference is removed from the received signal s. The singularvalues are the square roots of the nonzero eigenvalues of HH^(H) withrank min(M,N). Given that U is unitary, the noise variance of theorthogonalized system is unchanged with no noise enhancement.Accordingly, the optimal MIMO solution for spatial multiplexing can beexpressed as follows:

V=precoder,U ^(H)=equalizer

The description below provides background information on transmitdiversity schemes.

Ordinarily, maximum ratio combining (MRC) receivers are used; however,in LTE space frequency block codes are used. A block code is defined for2 transmit antennas and 4 transmit antennas, respectively, and thefollowing pertains to the LTE block code definitions thereof.

In the case of 2 antenna ports, pεE {0,1}, the frequency domain outputy(i)=[y⁽⁰⁾(i)y⁽¹⁾(i)]^(T), where i=0, 1, . . . , M_(symb) ^(ap)−1 is thecarrier index, of the transmitter precoding operation is defined by thefollowing expression:

$\begin{bmatrix}{y^{(0)}\left( {2} \right)} \\{y^{(1)}\left( {2} \right)} \\{y^{(0)}\left( {{2} + 1} \right)} \\{y^{(1)}\left( {{2} + 1} \right)}\end{bmatrix} = {{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 & j & 0 \\0 & {- 1} & 0 & j \\0 & 1 & 0 & j \\1 & 0 & {- j} & 0\end{bmatrix}}\begin{bmatrix}{{Re}\left( {x^{(0)}()} \right)} \\{{Re}\left( {x^{(1)}()} \right)} \\{{Im}\left( {x^{(0)}()} \right)} \\{{Im}\left( {x^{(1)}()} \right)}\end{bmatrix}}$

for i=0, 1, . . . , M_(symb) ^(layer)−1 with M_(symb) ^(ap)=2M_(symb)^(layer), where M_(symb) ^(layer) is the number of symbols per layer,and M_(symb) ^(ap) is the number of symbol per antenna port.

The superscript for y^((p))( ) indicates the antenna port number {0,1}.The operators Re( ) and Im( ) refer to the real and imaginary componentsof the complex precoder input signal x^((p))(i). For the case of twoantenna ports, there are two input signals, and the span of the precodercovers two adjacent frequency domain carriers using two antenna ports.The transmit precoder generates the IFFT modulator input signal in thefrequency domain.

The precoding operation can be rewritten showing permutation andmodification of the two transmit symbols x⁽⁰⁾(i) and x⁽¹⁾(i) on the twoantenna ports using adjacent frequency carriers as follows:

$\begin{bmatrix}{y^{(0)}\left( {2} \right)} \\{y^{(1)}\left( {2} \right)} \\{y^{(0)}\left( {{2} + 1} \right)} \\{y^{(1)}\left( {{2} + 1} \right)}\end{bmatrix} = {\frac{1}{\sqrt{2}}\begin{bmatrix}{x^{(0)}()} \\{- {{conj}\left( {x^{(1)}()} \right)}} \\{x^{(1)}()} \\{{conj}\left( {x^{(0)}()} \right)}\end{bmatrix}}$

where the conj( ) operator refers to the complex conjugate ofx^((p))(i).

In the case of 4 antenna ports, pε{0, 1, 2, 3}, the outputy(i)=[y⁽⁰⁾(i)y⁽¹⁾(i)y⁽²⁾(i)y⁽³⁾(i)]^(T), i=0, 1, . . . , M_(symb)^(ap)−1, of the transmitter precoding operation is defined by thefollowing expression:

$\quad{{\begin{bmatrix}{y^{(0)}\left( {4} \right)} \\{y^{(1)}\left( {4} \right)} \\{y^{(2)}\left( {4} \right)} \\{y^{(3)}\left( {4} \right)} \\{y^{(0)}\left( {{4} + 1} \right)} \\{y^{(1)}\left( {{4} + 1} \right)} \\{y^{(2)}\left( {{4} + 1} \right)} \\{y^{(3)}\left( {{4} + 1} \right)} \\{y^{(0)}\left( {{4} + 2} \right)} \\{y^{(1)}\left( {{4} + 2} \right)} \\{y^{(2)}\left( {{4} + 2} \right)} \\{y^{(3)}\left( {{4} + 2} \right)} \\{y^{(0)}\left( {{4} + 3} \right)} \\{y^{(1)}\left( {{4} + 3} \right)} \\{y^{(2)}\left( {{4} + 3} \right)} \\{y^{(3)}\left( {{4} + 3} \right)}\end{bmatrix} = {{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 & 0 & 0 & j & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {- 1} & 0 & 0 & 0 & j & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & j & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & {- j} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & j & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {- 1} & 0 & 0 & 0 & j \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & j \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & {- j} & 0\end{bmatrix}}\begin{bmatrix}{{Re}\left( {x^{(0)}()} \right)} \\{{Re}\left( {x^{(1)}()} \right)} \\{{Re}\left( {x^{(2)}()} \right)} \\{{Re}\left( {x^{(3)}()} \right)} \\{{Im}\left( {x^{(0)}()} \right)} \\{{Im}\left( {x^{(1)}()} \right)} \\{{Im}\left( {x^{(2)}()} \right)} \\{{Im}\left( {x^{(3)}()} \right)}\end{bmatrix}}{for}\mspace{14mu} i} = 0}},1,\ldots \;,{{M_{symb}^{layer} - {1\mspace{14mu} {with}M_{symb}^{ap}}} = \left\{ \begin{matrix}{4M_{symb}^{layer}} & {{{if}\mspace{14mu} M_{symb}^{(0)}{mod}\mspace{14mu} 4} = 0} \\{\left( {4M_{symb}^{layer}} \right) - 2} & {{{if}\mspace{14mu} M_{symb}^{(0)}{mod}\mspace{14mu} 4} \neq 0.}\end{matrix} \right.}}$

Once again, y^((p))(i) indicates the transmitter precoding output signalfor antenna p on carrier i as simply permutation and modification of thetransmitted symbols x^((q))(j). The precoder output feeds the IFFT inputin the frequency domain.

SUMMARY

Various embodiments of transmit diversity decoding algorithms aredescribed herein. The algorithms may be implemented in software,firmware, hardware, or any combination thereof. Furthermore, in order tosimplify the description, it is assumed that in all cases an LTE-Areceiver of the type shown in FIG. 2 is configured to present achannelization framework. This allows us to consider the frequencydomain MIMO channel system formulation from the frequency domain signalat the precoder in the far end transmitter to the frequency domainsignal at the FFT demodulator output in the receiver.

According to one aspect, a method may receive a first input thatincludes signals transmitted by M transmit antennas on C channels andreceived by N receive antennas, where M, N and C is each a positiveinteger greater than 1. The method may also receive a second input thatincludes estimates of channel matrix elements. Various methods areavailable to calculate channel matrix elements. Each channel matrixelement h(i,j), given as the matrix element of the channel matrix H,represents the transmission response in the frequency domain from thei^(th) transmit antenna to the j^(th) receiver antenna, generalized toinclude any possible filtering introduced by the modem either by analogor digital methods. Under this assumption, channel matrix elements canbe considered to be frequency scaling factors for the directtransmission channel and the interference channels. Training referencesignals are defined in the LTE signal and resource structure thatfacilitate this calculation. These methods are well-known to thoseskilled in the art of LTE modem design. The method may further generatean output that includes at least an estimate of a transmit signaltransmitted by one of the M transmit antennas on one of the C channelsbased at least in part on the first and the second inputs.

According to another aspect, a processor comprises a MIMO channelestimation module and a MIMO receiver processing module. The MIMOchannel estimation module may generate estimates of channel matrixelements with respect to C channels, C being a positive integer greaterthan 1. The MIMO receiver processing module, coupled to the MIMO channelestimation module, may receive a first input that includes signalstransmitted by M transmit antennas on the C channels and received by Nreceive antennas, where M and N is each a positive integer greaterthan 1. The MIMO receiver processing module may also receive, from theMIMO channel estimation module, a second input that includes theestimates of channel matrix elements with respect to C channels. TheMIMO receiver processing module may further generate an output thatincludes at least an estimate of a transmit signal transmitted by one ofthe M transmit antennas on one of the C channels based at least in parton the first and the second inputs.

According to a further aspect, a computer-readable medium may have a setof computer-executable instructions stored thereon. The instructions,when executed by one or more processors, may cause the one or moreprocessors to perform operations comprising: receiving a first inputthat includes signals transmitted by M transmit antennas on C channelsand received by N receive antennas, M, N and C each being a positiveinteger greater than 1; receiving a second input that includes estimatesof channel matrix elements; and generating an output that includes atleast an estimate of a transmit signal transmitted by one of the Mtransmit antennas on one of the C channels based at least in part on thefirst and the second inputs.

Thus, a robust and ideal decoder that implements one or more of theproposed algorithms may be developed for the transmit diversity schemedefined in the LTE standard.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more readily apparent to thoseordinarily skilled in the art after reviewing the following detaileddescription and accompanying drawings.

FIG. 1 is a flowchart of a transmit diversity decoding process inaccordance with an embodiment of the present disclosure.

FIG. 2 is a block diagram of components a processor in a receivercapable of implementing the transmit diversity decoding scheme inaccordance with the present disclosure.

FIG. 3 is a block diagram of a computing device capable of implementingthe transmit diversity decoding scheme in accordance with an embodimentof the present disclosure.

FIG. 4 is a block diagram of a single-input-single-output (SISO) systemin a single cell for a single user.

FIG. 5 is a block diagram of a multiple input, single output (MISO)system in a single cell for a single user.

FIG. 6 is a block diagram of a MIMO system in a single cell for a singleuser.

FIG. 7 is a block diagram of a MIMO system, or interference, in acooperative multi-cell environment for a single user.

FIG. 8 is a block diagram of a 2×2 transmit diversity decoder.

FIGS. 9 and 10 show block diagrams of a 4×2 transmit diversity decoder.

FIGS. 11, 12, 13, 14, and 15 show block diagrams of a 4×4 transmitdiversity decoder.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Overview

The proposed scheme uses diversity in the transmitter, i.e., thetransmission of identical, similar, or otherwise closely correlatedsignals, on appropriately spaced antennas, in order to compensate forthe frequency selective fading in the transmission signal path from thetransmitter side to the receiver side. The transmission path varies withtime as the transmitter, receiver, and the environment change. Thisvariation results in a time-varying channel frequency response, whichmay produce deep spectral nulls. In a single antenna transmissionscheme, there is only one signal and one signal path. A deep null undersuch circumstances would prevent reliable signal recovery at thereceiver.

Under the proposed transmit diversity scheme, multiple, i.e., different,signal paths from the transmitter side to the receiver side areconfigured such that one or more of the multiple signal paths wouldprovide an acceptable signal-to-noise ratio (SNR) and allow robustrecovery of the transmit signal in a channel environment which maycontain channel nulls or fades. That is, the techniques of the proposedscheme provide robust and ideal decoders for the transmit diversityscheme defined in the LTE standard. In the detailed description thatfollows, a respective decoder for each of three different M×N transmitdiversity cases is provided, where M denotes the number of transmitantennas and N denotes the number of receive antennas. A proof for eachcase demonstrating that each decoder provides ideal signal recoveryregardless of the channel matrix is also provided.

Exemplary 2×2 Transmit Diversity Case

In the expressions below, x=transmitter precoder input, y=transmitterprecoder output, H=channel matrix, r=receive signal, and s=detectedsignal.

The precoder operation can be rewritten as follows:

$\begin{bmatrix}{y^{(0)}\left( {2} \right)} & {y^{(0)}\left( {{2} + 1} \right)} \\{y^{(1)}\left( {2} \right)} & {y^{(1)}\left( {{2} + 1} \right)}\end{bmatrix} = \begin{bmatrix}{x(1)} & {x(2)} \\{- {x^{*}(2)}} & {x^{*}(1)}\end{bmatrix}$

The 1/√{square root over (2)} factor has been ignored since it justintroduces power scaling. Two symbols are transmitted using two antennasand two adjacent carriers on each antenna. The received signals areexpressed as follows, using a two-antenna port receiver:

$\begin{bmatrix}{r\left( {1,1} \right)} & {r\left( {1,2} \right)} \\{r\left( {2,1} \right)} & {r\left( {2,2} \right)}\end{bmatrix} = {\begin{bmatrix}{h\left( {1,1} \right)} & {h\left( {1,2} \right)} \\{h\left( {2,1} \right)} & {h\left( {2,2} \right)}\end{bmatrix}\begin{bmatrix}{y^{(0)}\left( {2} \right)} & {y^{(0)}\left( {{2} + 1} \right)} \\{y^{(1)}\left( {2} \right)} & {y^{(1)}\left( {{2} + 1} \right)}\end{bmatrix}}$

where

-   -   r(k,q)=the received signal on carrier (2i+q−1) and receiver port        number (k−1) for 1≦k≦2 and 1≦q≦2 and

The channel matrix is assumed to be ideal and the same for carrierfrequencies 2i and 2i+1. The channel matrix elements are indicated asfollows:

-   -   h(k,q)=the channel path transmission scaling factor in the        frequency domain at carrier frequencies 2i, 2i+1, 2i+2, and 2i+3        for the port (q−1) transmitter to the port (k−1) receiver for        1≦k≦2 and 1≦q≦2

The 2×2 decoder solution for the two symbols is expressed below, withs(1) being the decoder estimate of x(1) and s(2) being the decoderestimate of x(2), the * superscript indicates the complex conjugatemathematical operation and the |.|² operation indicates the magnitudesquared of the complex value:

s(1)=[h*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/D

s*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/D

D=|h(1,1)|² +|h(1,2)|² +|h(2,1)|² +|h(2,2)|²

Here, s(2) is simply the complex conjugate of the result calculatedabove as s*(2), requiring only a sign change for the imaginarycomponent. A block diagram of the 2×2 decoder is given in FIG. 8.

The proof below follows simple algebraic manipulation and substitution,and demonstrates that the 2×2 decoder provides ideal signal recoveryregardless of the channel matrix. Beginning with the equation for thedecoder estimate of the first symbol s(1) given by the presentinvention, the definition of the received signals for the 2×2 systemr(.,.), the transmit symbols defined by LTE, and the channel matrixelements h(.,.):

s(1)=[h*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/D

r(1,1)=h(1,1)y ⁽⁰⁾(2i)+h(1,2)y ⁽¹⁾(2i)

r(1,2)=h(1,1)y ⁽⁰⁾(2i+1)+h(1,2)y ⁽¹⁾(2i+1)

r(2,1)=h(2,1)y ⁽⁰⁾(2i)+h(2,2)y ⁽¹⁾(2i)

r(2,2)=h(2,1)y ⁽⁰⁾(2i+1)+h(2,2)y ⁽¹⁾(2i+1)

We substitute the received symbols into the equation for the symbolestimate as follows:

s(1)={h*(1,1)[h(1,1)y ⁽⁰⁾⁽2i)+h(1,2)y ⁽¹⁾(2i)]+h(1,2)[h*(1,1)y⁽⁰⁾*(2i+1)+h*(1,2)y ⁽¹⁾*(2i+1)]+h*(2,1)[h(2,1)y ⁽⁰⁾(2i)+h(2,2)y⁽¹⁾(2i)]+h(2,2)[h*(2,1)y ⁽⁰⁾*(2i+1)+h*(2,2)y ⁽¹⁾*(2i+1)]}/D

Simplify using the algebraic distributive property:

s(1)={h*(1,1)h(1,1)y ⁽⁰⁾(2i)+h*(1,1)h(1,2)y ⁽¹⁾(2i)+h(1,2)h*(1,1)y⁽⁰⁾*(2i+1)+h(1,2)h*(1,2)y ⁽¹⁾*(2i+1)+h*(2,1)h(2,1)y⁽⁰⁾*(2i+1)+h(2,1)h(2,2)y ⁽¹⁾(2i)]+h(2,2)h*(2,1)y⁽⁰⁾*(2i+1)+h(2,2)h*(2,2)y ⁽¹⁾*(2i+1)]}/D

Next recognize that |h(i,j)|²=h(i,j)h*(i,j):

s(1)={|h(1,1)|² y ⁽⁰⁾(2i)+h*(1,1)h(1,2)y ⁽¹⁾(2i)+h(1,2)h*(1,1)y⁽⁰⁾*(2i+1)+|h(1,2)|² y ⁽¹⁾*(2i+1)+|h(2,1)|² y ⁽⁰⁾(2i)+h*(2,1)h(2,2)y⁽¹⁾(2i)]+h(2,2)h*(2,1)y ⁽⁰⁾*(2i+1)+|h(2,2)|² y ⁽¹⁾*(2i+1)]}/D

Now notice the following definitions, substitute, and simplify:

y ⁽⁰⁾(2i)=x(1)

y ⁽¹⁾(2i)=−x*(2)

y ⁽⁰⁾*(2i+1)=x*(2)

y ⁽¹⁾*(2i+1)=x(1)

s(1)={|h(1,1)|² x(1)−h*(1,1)h(1,2)x*(2)+h(1,2)h*(1,1)x*(2)+|h(1,2)|²x(1)+|h(2,1)|² x(1)−h*(2,1)h(2,2)x*(2)]+h(2,2)h*(2,1)x*(2)+|h(2,2)|²x(1)]}/D

s(1)={|h(1,1)|² x(1)+|h(1,2)|² x(1)+|h(2,1)|² x(1)+|h(2,2)|² x(1)]}/D

s(1)=x(1)[|h(1,1)|² +|h(1,2)|² x(1)+|h(2,1)|² +|h(2,2)|² ]/D=x(1)D/D

→s(1)=x(1)

This completes the proof that the 2×2 system decoder estimate of thefirst symbol s(1) is the actual transmitted symbol x(1), given thecorrect channel matrix estimate H. Now consider the decoder estimate forthe second symbol:

s*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/D

Again, following the same method to establish a proof for this secondsymbol, we show the equations for the received signals as a function ofthe transmitted signals and the channel matrix elements:

r(1,1)=h(1,1)y ⁽⁰⁾(2i)+h(1,2)y ⁽¹⁾(2i)=h(1,1)x(1)−h(1,2)x*(2)

r(1,2)=h(1,1)y ⁽⁰⁾(2i+1)+h(1,2)y ⁽¹⁾(2i+1)=h(1,1)x(2)+h(1,2)x*(1)

r(2,1)=h(2,1)y ⁽⁰⁾(2i)+h(2,2)y ⁽¹⁾(2i)=h(2,1)x(1)−h(2,2)x*(2)

r(2,2)=h(2,1)y ⁽⁰⁾(2i+1)+h(2,2)y ⁽¹⁾(2i+1)=h(2,1)x(2)+h(2,2)x*(1)

Substitute these expressions into the equation for the symbol estimate:

s*(2)={−h*(1,2)[h(1,1)x(1)−h(1,2)x*(2)]+h(1,1)[h*(1,1)x*(2)+h*(1,2)x(1)]−h*(2,2)[h(2,1)x(1)−h(2,2)x*(2)]+h(2,1)[h*(2,1)x*(2)+h*(2,2)x(1)]}/D

Apply the distributive property and simplify:

s*(2)=[−h*(1,2)h(1,1)x(1)+h*(1,2)h(1,2)x*(2)+h(1,1)h*(1,1)x*(2)+h(1,1)h*(1,2)x(1)−h*(2,2)h(2,1)x(1)+h*(2,2)h(2,2)x*(2)+h(2,1)h*(2,1)x*(2)+h(2,1)h*(2,2)x(1)]/D

s*(2)=[h*(1,2)h(1,2)x*(2)+h(1,1)h*(1,1)x*(2)+h*(2,2)h(2,2)x*(2)+h(2,1)h*(2,1)x*(2)]/D

s*(2)=[|h(1,2)|² x*(2)+|h(1,1)|² x*(2)+|h(2,2)|² x*(2)+|h(2,1)|²x*(2)]/D

s*(2)=x*(2)[|h(1,2)|² +|h(1,1)|² +|h(2,2)|² +|h(2,1)|² ]/D

s*(2)=x*(2)D/D=x*(2)

→s(2)=x(2)

This completes the proof showing that the decoder estimate for thesecond symbol is equal to the actual transmitted symbol, given theproper channel matrix estimate.

Exemplary 4×2 Transmit Diversity Case

In the expressions below, x=precoder input, y=precoder output, H=channelmatrix, r=receive signal, and s=detected signal.

The precoder operation can be rewritten as follows:

$\quad{\begin{bmatrix}{y^{(0)}\left( {2} \right)} & {y^{(0)}\left( {{2} + 1} \right)} & {y^{(0)}\left( {{2} + 2} \right)} & {y^{(0)}\left( {{2} + 3} \right)} \\{y^{(1)}\left( {2} \right)} & {y^{(1)}\left( {{2} + 1} \right)} & {y^{(1)}\left( {{2} + 2} \right)} & {y^{(1)}\left( {{2} + 3} \right)} \\{y^{(2)}\left( {2} \right)} & {y^{(2)}\left( {{2} + 1} \right)} & {y^{(2)}\left( {{2} + 2} \right)} & {y^{(2)}\left( {{2} + 3} \right)} \\{y^{(3)}\left( {2} \right)} & {y^{(3)}\left( {{2} + 1} \right)} & {y^{(3)}\left( {{2} + 2} \right)} & {y^{(3)}\left( {{2} + 3} \right)}\end{bmatrix} = {\quad\begin{bmatrix}{x(1)} & {x(2)} & 0 & 0 \\0 & 0 & {x(3)} & {x(4)} \\{- {x^{*}(2)}} & {x^{*}(1)} & 0 & 0 \\0 & 0 & {- {x^{*}(4)}} & {x^{*}(3)}\end{bmatrix}}}$

Four symbols are transmitted using four antennas and four adjacentcarriers on each antenna. The received signals are expressed as follows,using four adjacent carriers and two receiver antenna ports:

$\begin{bmatrix}{r\left( {1,1} \right)} & {r\left( {1,2} \right)} & {r\left( {1,3} \right)} & {r\left( {1,4} \right)} \\{r\left( {2,1} \right)} & {r\left( {2,2} \right)} & {r\left( {2,3} \right)} & {r\left( {2,4} \right)}\end{bmatrix} = {\begin{bmatrix}{h\left( {1,1} \right)} & {h\left( {1,2} \right)} & {h\left( {1,3} \right)} & {h\left( {1,4} \right)} \\{h\left( {2,1} \right)} & {h\left( {2,2} \right)} & {h\left( {2,3} \right)} & {h\left( {2,4} \right)}\end{bmatrix}{\quad\begin{bmatrix}{y^{(0)}\left( {2} \right)} & {y^{(0)}\left( {{2} + 1} \right)} & {y^{(0)}\left( {{2} + 2} \right)} & {y^{(0)}\left( {{2} + 3} \right)} \\{y^{(1)}\left( {2} \right)} & {y^{(1)}\left( {{2} + 1} \right)} & {y^{(1)}\left( {{2} + 2} \right)} & {y^{(1)}\left( {{2} + 3} \right)} \\{y^{(2)}\left( {2} \right)} & {y^{(2)}\left( {{2} + 1} \right)} & {y^{(2)}\left( {{2} + 2} \right)} & {y^{(2)}\left( {{2} + 3} \right)} \\{y^{(3)}\left( {2} \right)} & {y^{(3)}\left( {{2} + 1} \right)} & {y^{(3)}\left( {{2} + 2} \right)} & {y^{(3)}\left( {{2} + 3} \right)}\end{bmatrix}}}$

where

-   -   r(k,q)=the received signal on carrier (2i+q−1) and receiver port        number (k−1) for 1≦k≦2 and 1≦q≦4.

The channel matrix is assumed to be ideal and the same for carrierfrequencies 2i, 2i+1, 2i+2 and 2i+3. The channel matrix elements areindicated as follows:

-   -   h(k,q)=the channel path transmission scaling factor in the        frequency domain at carrier frequencies 2i, 2i+1, 2i+2, and 2i+3        for the port (q−1) transmitter to the port (k−1) receiver for        1≦k≦2 and 1≦q≦4.

The 4×2 decoder solution for four symbols is expressed below, with s(1)being the decoder estimate of x(1), . . . , and s(4) being the decoderestimate of x(4):

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)]/D(1)

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)]/D(1)

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)]/D(2)

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)]/D(2)

D(1)=|h(1,1)|² +|h(1,3)|² +|h(2,1)|² +|h(2,3)|²

D(2)=|h(1,2)|² +|h(1,4)|² +|h(2,2)|² +|h(2,4)|²

The block diagram for the 4×2 transmit diversity decoder is a straightforward extension of the block diagram shown in FIG. 8 for the 2×2system, extended for the additional terms with the appropriatemodifications indicated by the equations, and is shown in FIGS. 9 and10.

The proof below follows simple algebraic substitution and manipulation,and demonstrates that the 4×2 decoder provides ideal signal recoveryregardless of the channel matrix.

Start with:

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)]/D(1)

The received signals for the 4×2 system follow as:

r(1,1)=h(1,1)x(1)−h(1,3)x*(2)

r(1,2)=h(1,1)x(2)+h(1,3)x*(1)

r(2,1)=h(2,1)x(1)−h(2,3)x*(2)

r(2,2)=h(2,1)x(2)+h(2,3)x*(1)

Substitution and simplification follow:

s(1)={h*(1,1)[h(1,1)x(1)−h(1,3)x*(2)]+h(1,3)[h*(1,1)x*(2)+h*(1,3)x(1)]+h*(2,1)[h(2,1)x(1)−h(2,3)x*(2)]+h(2,3)[h*(2,1)x*(2)+h*(2,3)x(1)]}D(1)

Apply the distributive property and simplify as follows:

s(1)=[h*(1,1)h(1,1)x(1)−h*(1,1)h(1,3)x*(2)+h(1,3)h*(1,1)x*(2)+h(1,3)h*(1,3)x(1)+h*(2,1)h(2,1)x(1)−h*(2,1)h(2,3)x*(2)+h(2,3)h*(2,1)x*(2)+h(2,3)h*(2,3)x(1)]/D(1)

s(1)=[|h(1,1)|² x(1)+|h(1,3)|² x(1)+|h(2,1)|² x(1)+|h(2,3)|² x(1)]/D(1)

Complete the proof for the first symbol:

→s(1)=x(1)

Consider the estimate for the second symbol and follow the same methodfor the proof:

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)]/D(1)

s*(2)=[−h*(1,3)[h(1,1)x(1)−h(1,3)x*(2)]+h(1,1)[h*(1,1)x*(2)+h*(1,3)x(1)]−h*(2,3)[h(2,1)x(1)−h(2,3)x*(2)]+h(2,1)[h*(2,1)x*(2)+h*(2,3)x(1)]]/D(1)

s*(2)=[−h*(1,3)h(1,1)x(1)+h*(1,3)h(1,3)x*(2)+h(1,1)h*(1,1)x*(2)+h(1,1)h*(1,3)x(1)−h*(2,3)h(2,1)x(1)+h*(2,3)h(2,3)x*(2)+h(2,1)h*(2,1)x*(2)+h(2,1)h*(2,3)x(1)]/D(1)

s*(2)=[|h(1,3)|² x*(2)+|h(1,1)|² x*(2)+|h(2,3)|² x*(2)+|h(2,1)|²x*(2)]/D(1)

→s(2)=x(2)

This completes the proof for the second symbol. Now consider the thirdsymbol and once again follow the same approach as above:

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)]/D(2)

r(1,3)=h(1,2)x(3)−h(1,4)x*(4)

r(1,4)=h(1,2)x(4)+h(1,4)x*(3)

r(2,3)=h(2,2)x(3)−h(2,4)x*(4)

r(2,4)=h(2,2)x(4)+h(2,4)x*(3)

s(3)=[h*(1,2)[h(1,2)x(3)−h(1,4)x*(4)]+h(1,4)[h*(1,2)x*(4)+h*(1,4)x(3)]+h*(2,2)[h(2,2)x(3)−h(2,4)x*(4)]+h(2,4)[h*(2,2)x*(4)+h*(2,4)x(3)]]/D(2)

s(3)=[h*(1,2)h(1,2)x(3)−h*(1,2)h(1,4)x*(4)+h(1,4)h*(1,2)x*(4)+h(1,4)h*(1,4)x(3)+h*(2,2)h(2,2)x(3)−h*(2,2)h(2,4)x*(4)+h(2,4)h*(2,2)x*(4)+h(2,4)h*(2,4)x(3)]/D(2)

s(3)=[|h(1,2)|² x(3)+|h(1,4)|² x(3)+|h(2,2)|² x(3)+|h(2,4)|² x(3)]/D(2)

→s(3)=x(3)

This completes the proof for the third symbol. Now consider the forthsymbol and once again follow the same approach as above:

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)]/D(2)

s*(4)={−h*(1,4)[h(1,2)x(3)−h(1,4)x*(4)]+h(1,2)[h*(1,2)x*(4)+h*(1,4)x(3)]−h*(2,4)[h(2,2)x(3)−h(2,4)x*(4)]+h(2,2)[h*(2,2)x*(4)+h*(2,4)x(3)]}/D(2)

s*(4)={−h*(1,4)h(1,2)x(3)+h*(1,4)h(1,4)x*(4)+h(1,2)h*(1,2)x*(4)+h(1,2)h*(1,4)x(3)−h*(2,4)h(2,2)x(3)+h*(2,4)h(2,4)x*(4)]+h(2,2)h*(2,2)x*(4)+h(2,2)h*(2,4)x(3)]}/D(2)

s*(4)=[|h(1,4)|² x*(4)+|h(1,2)|² x*(4)+|h(2,4)|² x*(4)]+|h(2,2)|²x*(4)]/D(2)

→s(4)=x(4)

This completes the proof for the third symbol.

Exemplary 4×4 Transmit Diversity Case

In the expressions below, x=precoder input, y=precoder output, H=channelmatrix, r=receive signal, and s=detected signal.

The precoder operation can be rewritten as follows:

$\begin{bmatrix}{y^{(0)}\left( {2} \right)} & {y^{(0)}\left( {{2} + 1} \right)} & {y^{(0)}\left( {{2} + 2} \right)} & {y^{(0)}\left( {{2} + 3} \right)} \\{y^{(1)}\left( {2} \right)} & {y^{(1)}\left( {{2} + 1} \right)} & {y^{(1)}\left( {{2} + 2} \right)} & {y^{(1)}\left( {{2} + 3} \right)} \\{y^{(2)}\left( {2} \right)} & {y^{(2)}\left( {{2} + 1} \right)} & {y^{(2)}\left( {{2} + 2} \right)} & {y^{(2)}\left( {{2} + 3} \right)} \\{y^{(3)}\left( {2} \right)} & {y^{(3)}\left( {{2} + 1} \right)} & {y^{(3)}\left( {{2} + 2} \right)} & {y^{(3)}\left( {{2} + 3} \right)}\end{bmatrix} = {\quad\begin{bmatrix}{x(1)} & {x(2)} & 0 & 0 \\0 & 0 & {x(3)} & {x(4)} \\{- {x^{*}(2)}} & {x^{*}(1)} & 0 & 0 \\0 & 0 & {- {x^{*}(4)}} & {x^{*}(3)}\end{bmatrix}}$

Four symbols are transmitted using four antennas and four adjacentcarriers on each antenna. The received signals are expressed as followsfor four adjacent carriers and four receive antenna port:

$\begin{bmatrix}{r\left( {1,1} \right)} & {r\left( {1,2} \right)} & {r\left( {1,3} \right)} & {r\left( {1,4} \right)} \\{r\left( {2,1} \right)} & {r\left( {2,2} \right)} & {r\left( {2,3} \right)} & {r\left( {2,4} \right)} \\{r\left( {3,1} \right)} & {r\left( {3,2} \right)} & {r\left( {3,3} \right)} & {r\left( {3,4} \right)} \\{r\left( {4,1} \right)} & {r\left( {4,2} \right)} & {r\left( {4,3} \right)} & {r\left( {4,4} \right)}\end{bmatrix} = {\begin{bmatrix}{h\left( {1,1} \right)} & {h\left( {1,2} \right)} & {h\left( {1,3} \right)} & {h\left( {1,4} \right)} \\{h\left( {2,1} \right)} & {h\left( {2,2} \right)} & {h\left( {2,3} \right)} & {h\left( {2,4} \right)} \\{h\left( {3,1} \right)} & {h\left( {3,2} \right)} & {h\left( {3,3} \right)} & {h\left( {3,4} \right)} \\{h\left( {4,1} \right)} & {h\left( {4,2} \right)} & {h\left( {4,3} \right)} & {h\left( {4,4} \right)}\end{bmatrix}{\quad\begin{bmatrix}{y^{(0)}\left( {2} \right)} & {y^{(0)}\left( {{2} + 1} \right)} & {y^{(0)}\left( {{2} + 2} \right)} & {y^{(0)}\left( {{2} + 3} \right)} \\{y^{(1)}\left( {2} \right)} & {y^{(1)}\left( {{2} + 1} \right)} & {y^{(1)}\left( {{2} + 2} \right)} & {y^{(1)}\left( {{2} + 3} \right)} \\{y^{(2)}\left( {2} \right)} & {y^{(2)}\left( {{2} + 1} \right)} & {y^{(2)}\left( {{2} + 2} \right)} & {y^{(2)}\left( {{2} + 3} \right)} \\{y^{(3)}\left( {2} \right)} & {y^{(3)}\left( {{2} + 1} \right)} & {y^{(3)}\left( {{2} + 2} \right)} & {y^{(3)}\left( {{2} + 3} \right)}\end{bmatrix}}}$

where

-   -   r(k,q)=the received signal on carrier (2i+q−1) and receiver port        number (k−1) for 1≦k≦4 and 1≦q≦4.

The channel matrix is assumed to be ideal and the same for carrierfrequencies 2i, 2i+1, 2i+2 and 2i+3. The channel matrix elements areindicated as follows:

-   -   h(k,q)=the channel path transmission scaling factor in the        frequency domain at carrier frequencies 2i, 2i+1, 2i+2, and 2i+3        for the port (q−1) transmitter to the port (k−1) receiver for 1        and 1

The 4×4 decoder estimate solution for four symbols is expressed below,with s(1) being the estimate of x(1), . . . , and s(4) being theestimate of x(4):

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)−h*(3,3)r(3,1)+h(3,1)r*(3,2)−h*(4,3)r(4,1)+h(4,1)r*(4,2)]/D(1)

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)+h*(3,2)r(3,3)+h(3,4)r*(3,4)+h*(4,2)r(4,3)+h(4,4)r*(4,4)]/D(2)

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)−h*(3,4)r(3,3)+h(3,2)r*(3,4)−h*(4,4)r(4,3)+h(4,2)r*(4,4)]/D(2)

D(1)=|h(1,1)|² +|h(2,1)|² +|h(1,3)|² |h(2,3)|² +|h(3,1)|² +|h(3,3)|²+|h(4,1)|² +|h(4,3)|²

D(2)=|h(1,2)|² +|h(2,2)|² +|h(1,4)|² +|h(2,4)|² +|h(3,2)|² +|h(3,4)|²+|h(4,2)|² +|h(4,4)|²

A block diagram for the 4×4 transmit diversity decoder is shown in FIGS.11, 12, 13, 14, and 15.

The proof below follows simple algebraic manipulation, and demonstratesthat the 4×4 decoder provides ideal signal recovery regardless of thechannel matrix. The list of received signal equations below results fromthe matrix multiplication above using the equation for the precoder andthe channel matrix operation:

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)

r(1,1)=h(1,1)x(1)−h(1,3)x*(2)

r(1,2)=h(1,1)x(2)+h(1,3)x*(1)

r(2,1)=h(2,1)x(1)−h(2,3)x*(2)

r(2,2)=h(2,1)x(2)+h(2,3)x*(1)

r(1,3)=h(1,2)x(3)−h(1,4)x*(4)

r(1,4)=h(1,2)x(4)+h(1,4)x*(3)

r(2,3)=h(2,2)x(3)−h(2,4)x*(4)

r(2,4)=h(2,2)x(4)+h(2,4)x*(3)

r(3,1)=h(3,1)x(1)−h(3,3)x*(2)

r(3,2)=h(3,1)x(2)+h(3,3)x*(1)

r(4,1)=h(4,1)x(1)−h(4,3)x*(2)

r(4,2)=h(4,1)x(2)+h(4,3)x*(1)

r(3,3)=h(3,2)x(3)−h(3,4)x*(4)

r(3,4)=h(3,2)x(4)+h(3,4)x*(3)

r(4,3)=h(4,2)x(3)−h(4,4)x*(4)

r(4,4)=h(4,2)x(4)+h(4,4)x*(3)

s(1)={h*(1,1)[h(1,1)x(1)−h(1,3)x*(2)]+h(1,3)[h*(1,1)x*(2)+h*(1,3)x(1)]+h*(2,1)[h(2,1)x(1)−h(2,3)x*(2)]+h(2,3)[h*(2,1)x*(2)+h*(2,3)x(1)]+h*(3,1)[h(3,1)x(1)−h(3,3)x*(2)]+h(3,3)[h*(3,1)x*(2)+h*(3,3)x(1)]+h*(4,1)[h(4,1)x(1)−h(4,3)x*(2)]+h(4,3)[h*(4,1)x*(2)+h*(4,3)x(1)]}/D(1)

s(1)=[h*(1,1)h(1,1)x(1)−h*(1,1)h(1,3)x*(2)+h(1,3)h*(1,1)x*(2)+h(1,3)h*(1,3)x(1)+h*(2,1)h(2,1)x(1)−h*(2,1)h(2,3)x*(2)+h(2,3)h*(2,1)x*(2)+h(2,3)h*(2,3)x(1)+h*(3,1)h(3,1)x(1)−h*(3,1)h(3,3)x*(2)+h(3,3)h*(3,1)x*(2)+h(3,3)h*(3,3)x(1)+h*(4,1)h(4,1)x(1)−h*(4,1)h(4,3)x*(2)+h(4,3)h*(4,1)x*(2)+h(4,3)h*(4,3)x(1)]/D(1)

s(1)=[|h(1,1)|² x(1)+|h(1,3)|² x(1)+|h(2,1)|² x(1)+|h(2,3)|²x(1)+|h(3,1)|² x(1)+|h(3,3)|² x(1)|h(4,1)|² x(1)+|h(4,3)|² x(1)]/D(1)

→s(1)=x(1)

s*(2)=[−h*(1,3)[h(1,1)x(1)−h(1,3)x*(2)]+h(1,1)[h*(1,1)x*(2)+h*(1,3)x(1)]−h*(2,3)[h(2,1)x(1)−h(2,3)x*(2)]+h(2,1)[h*(2,1)x*(2)+h*(2,3)x(1)]−h*(3,3)[h(3,1)x(1)−h(3,3)x*(2)]+h(3,1)[h*(3,1)x*(2)+h*(3,3)x(1)]−h*(4,3)[h(4,1)x(1)−h(4,3)x*(2)]+h(4,1)[h*(4,1)x*(2)+h*(4,3)x(1)]]/D(1)

s*(2)=[−h*(1,3)h(1,1)x(1)+h*(1,3)h(1,3)x*(2)+h(1,1)h*(1,1)x*(2)+h(1,1)h*(1,3)x(1)−h*(2,3)h(2,1)x(1)+h*(2,3)h(2,3)x*(2)+h(2,1)h*(2,1)x*(2)+h(2,1)h*(2,3)x(1)−h*(3,3)h(3,1)x(1)+h*(3,3)h(3,3)x*(2)+h(3,1)h*(3,1)x*(2)+h(3,1)h*(3,3)x(1)−h*(4,3)h(4,1)x(1)+h*(4,3)h(4,3)x*(2)+h(4,1)h*(4,1)x*(2)+h(4,1)h*(4,3)x(1)]/D(1)

s*(2)=[|h(1,3)|² x*(2)+|h(1,1)|² x*(2)+|h(2,3)|² x*(2)+|h(2,1)|²x*(2)+|h(3,3)|² x*(2)+|h(3,1)|² x*(2)+|h(4,3)|² x*(2)+|h(4,1)|²x*(2)]/D(1)

→s(2)=x(2)

s(3)=[h*(1,2)[h(1,2)x(3)−h(1,4)x*(4)]+h(1,4)[h*(1,2)x*(4)+h*(1,4)x(3)]+h*(2,2)[h(2,2)x(3)−h(2,4)x*(4)]+h(2,4)[h*(2,2)x*(4)+h*(2,4)x(3)]+h*(3,2)[h(3,2)x(3)−h(3,4)x*(4)]+h(3,4)[h*(3,2)x*(4)+h*(3,4)x(3)]+h*(4,2)[h(4,2)x(3)−h(4,4)x*(4)]+h(4,4)[h*(4,2)x*(4)+h*(4,4)x(3)]]/D(2)

s(3)=[h*(1,2)h(1,2)x(3)−h*(1,2)h(1,4)x*(4)+h(1,4)h*(1,2)x*(4)+h(1,4)h*(1,4)x(3)+h*(2,2)h(2,2)x(3)−h*(2,2)h(2,4)x*(4)+h(2,4)h*(2,2)x*(4)+h(2,4)h*(2,4)x(3)+h*(3,2)h(3,2)x(3)−h*(3,2)h(3,4)x*(4)+h(3,4)h*(3,2)x*(4)+h(3,4)h*(3,4)x(3)+h*(4,2)h(4,2)x(3)−h*(4,2)h(4,4)x*(4)+h(4,4)h*(4,2)x*(4)+h(4,4)h*(4,4)x(3)]/D(2)

s(3)=[|h(1,2)|² x(3)+|h(1,4)|² x(3)+|h(2,2)|² x(3)+|h(2,4)|²x(3)+|h(3,2)|² x(3)+|h(3,4)|² x(3)+|h(4,2)|² x(3+|h(4,4)|² x(3)]/D(2)

→s(3)=x(3)

s*(4)=[−h*(1,4)[h(1,2)x(3)−h(1,4)x*(4)]+h(1,2)[h*(1,2)x*(4)+h*(1,4)x(3)]−h*(2,4)[h(2,2)x(3)−h(2,4)x*(4)]+h(2,2)[h*(2,2)x*(4)+h*(2,4)x(3)]−h*(3,4)[h(3,2)x(3)−h(3,4)x*(4)]+h(3,2)[h*(3,2)x*(4)+h*(3,4)x(3)]−h*(4,4)[h(4,2)x(3)−h(4,4)x*(4)]+h(4,2)[h*(4,2)x*(4)+h*(4,4)x(3)]]/D(2)

s*(4)=[−h*(1,4)h(1,2)x(3)+h*(1,4)h(1,4)x*(4)+h(1,2)h*(1,2)x*(4)+h(1,2)h*(1,4)x(3)−h*(2,4)h(2,2)x(3)+h*(2,4)h(2,4)x*(4)+h(2,2)h*(2,2)x*(4)+h(2,2)h*(2,4)x(3)−h*(3,4)h(3,2)x(3)+h*(3,4)h(3,4)x*(4)+h(3,2)h*(3,2)x*(4)+h(3,2)h*(3,4)x(3)−h*(4,4)h(4,2)x(3)+h*(4,4)h(4,4)x*(4)+h(4,2)h*(4,2)x*(4)+h(4,2)h*(4,4)x(3)]/D(2)

s*(4)=[|h(1,4)|² x*(4)+|h(1,2)|² x*(4)+|h(2,4)|² x*(4)+|h(2,2)|² x*(4)+

|h(3,4)|² x*(4)+|h(3,2)|² x*(4)+|h(4,4)|² x*(4)+|h(4,2)|² x*(4)]/D(2)

→s(4)=x(4)

Exemplary Process

FIG. 1 illustrates a flowchart of a transmit diversity decoding process100 in accordance with an embodiment of the present disclosure. In oneor more embodiments, one or more of the operations of the process 100may be omitted, repeated, and/or performed in a different order.Accordingly, the specific arrangement of operations shown in FIG. 1 isnot to be construed as limiting the scope of the technique.

The process 100 may begin at 102. At 102, the process receives a firstinput that includes signals transmitted by M transmit antennas on Cchannels and received by N receive antennas, where M, N and C is each apositive integer greater than 1. At 104, the process receives a secondinput that includes estimates of channel matrix elements. At 106, theprocess generates an output that includes an estimate of a transmitsignal transmitted by all of the M transmit antennas on all of the Cchannels based at least in part on the first and the second inputs.

In one embodiment, generating an output that includes at least anestimate of a transmit signal transmitted by all of the M transmitantennas on all of the C channels comprises generating an output thatincludes a plurality of estimates of transmit signals transmitted bysome or all of the M transmit antennas on some or all of the C channels.

In one embodiment, when M=2 and N=2, generating an output that includesat least an estimate of both transmit symbols transmitted by both of the2 transmit antennas on all of the 4 channels comprises generating theoutput according to an algorithm expressed as follows:

s(1)=[h*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/D

s*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/D

-   -   where    -   D=|h(1,1)|²+|h(1,2)|²+|h(2,1)|²+|h(2,2)|²

Here, s(1) is the decoder estimate of the transmitted symbol x(1), ands(2) is the decoder estimate of the transmitted symbol x(2). The channelmatrix elements are given as h(i,j).

In one embodiment, when M=4 and N=2, generating an output that includesat least an estimate of all transmit symbols transmitted by all of the 4transmit antennas on all of the 8 channels comprises generating theoutput according to an algorithm expressed as follows:

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)]/D(1)

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)]/D(1)

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)]/D(2)

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)]/D(2)

-   -   where    -   D(1)=|h(1,1)|²+|h(1,3)|²+|h(2,1)|²+|h(2,3)|²    -   D(2)=|h(1,2)|²+|h(1,4)|²+|h(2,2)|²+|h(2,4)|²

In one embodiment, when M=4 and N=4, generating an output that includesat least an estimate of all 4 transmit symbols transmitted by all of the4 transmit antennas on all of the 16 channels comprises generating theoutput according to an algorithm expressed as follows:

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)−h*(3,3)r(3,1)+h(3,1)r*(3,2)−h*(4,3)r(4,1)+h(4,1)r*(4,2)]/D(1)

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)+h*(3,2)r(3,3)+h(3,4)r*(3,4)+h*(4,2)r(4,3)+h(4,4)r*(4,4)]/D(2)

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)−h*(3,4)r(3,3)+h(3,2)r*(3,4)−h*(4,4)r(4,3)+h(4,2)r*(4,4)]/D(2)

-   -   where    -   D(1)=|h(1,1)|²+|h(2,1)|²+|h(1,3)|²+|h(2,3)|²+|h(3,1)|²+|h(3,3)|²+|h(4,1)|²+|h(4,3)|²    -   D(2)=|h(1,2)|²+|h(2,2)|²+|h(1,4)|²+|h(2,4)|²+|h(3,2)|²+|h(3,4)|²+|h(4,2)|²+|h(4,4)|²

The process 100 or any variations thereof may be carried out as a resultof executing computer-executable instructions, e.g., computerprogramming codes, stored on one or more non-transitorycomputer-readable medium, herein interchangeably referred to ascomputer-readable storage medium, by a processor, a central processingunit, a computing device such as, for example, the computing device 300of FIG. 3. Such one or more computer-readable medium may be one or moretangible storage device including, but not limited to, random accessmemory (RAM), read-only memory (ROM), electrically erasable programmableread-only memory (EEPROM), flash memory or other memory technology,compact disc read-only memory (CD-ROM), digital versatile disks (DVD),any optical storage, magnetic cassettes, magnetic tape, magnetic diskstorage or other magnetic storage devices, or any other non-transitorymedium which can be used to store the desired information now known orlater developed and which can be accessed by a processor, a centralprocessing unit, a computing device such as, for example, the computingdevice 300 of FIG. 3. In the present disclosure, the term “one or morecomputer-readable medium” does not encompass any non-tangible ortransitory propagating signal such as, for example, electromagnetic oracoustic signal or waveform and shall not be interpreted as such.

Illustrative Receiver

FIG. 2 illustrates components of a processor 200 in a receiver that iscapable of implementing the transmit diversity decoding scheme inaccordance with the present disclosure, including the process 100 andany variation thereof. The components of the processor 200 depicted inFIG. 2 are for one component carrier. As the same design and operatingprinciple described and depicted herein can be repeated and used formultiple component carriers, in the interest of brevity components formultiple component carriers will not be illustrated or described.

As shown in FIG. 2, the processor 200 comprises a MIMO receiverprocessing module 202 and a MIMO channel estimation module 204. The MIMOchannel estimation module 204 is configured to generate estimates ofchannel matrix elements with respect to C channels, where C is apositive integer greater than 1. The MIMO receiver processing module 202is coupled to the MIMO channel estimation module 204. The MIMO receiverprocessing module 202 is configured to receive a first input thatincludes signals transmitted by M transmit antennas on the C channelsand received by N receive antennas, where M and N is each a positiveinteger greater than 1. The MIMO receiver processing module 202 is alsoconfigured to receive, from the MIMO channel estimation module, a secondinput that includes the estimates of channel matrix elements withrespect to C channels. The MIMO receiver processing module 202 isfurther configured to generate an output that includes at least anestimate of a transmit signal transmitted by one of the M transmitantennas on one of the C channels based at least in part on the firstand the second inputs.

The MIMO channel estimation module 204 calculates the transmissionchannel matrix by using a number of reference signals that are embeddedin the signal and resource structure. The reference signals are known tothe receiver and are interspersed in both time and frequency. For eachcarrier, wherever the reference signals are located on thetime/frequency/antenna resource grid, the signal on all other antennaports corresponding to the same time and frequency position is set tozero to eliminate interference from the other antennas. By doing so, thetransmission path from the active transmit antenna port to all thepossible receive antenna ports can be calculated. This allowscalculation of all of the possible channel matrix elements from eachtransmitter port to each receiver port, completing the channel matrix.

The processor 200 may also comprise a frequency offset compensation(FOC) module 206, a first-in, first-out (FIFO) sample buffer 208, a fastFourier transform (FFT) demodulator 210, a resource element demapper212, a modulation demapping, descrambling and soft slicing module 214, arate matching recovery module 216, a turbo decoder 218, a code blockdesegment cyclic redundancy check (CRC) module 220, a layer 2/3processing module 222, a primary synchronization signal filtering,buffering and detection module 224.

The frequency offset compensation module 206 adjusts the sample timingof the receiver to match that of the far end transmitter. It does thisby using a poly-phase filter with interpolated re-timing of the samplingprocess. It then branches to feed the primary synchronization signalfiltering, buffering and detection module 224, which is a detectionmechanism for the primary synchronization signal. The first-in,first-out (FIFO) sample buffer 208 is written with new samples as theyare received, and the oldest samples are removed for further digitalprocessing. Following the first-in, first-out (FIFO) sample buffer 208is the fast Fourier transform demodulator 210. Multicarrier transmissionschemes such as dual-mode transmitter (DMT) and OFDM use the inverse FFTas the signal modulator and the FFT as the demodulator. Following thefast Fourier transform demodulator 210 is the resource element demapper212, which extracts data from specific locations across time andfrequency, as allocated by a high level resource management algorithm.

At this point the MIMO processing functionality, which is partiallycovered by the material in this application, is addressed. The output ofthe MIMO receiver processing module 202 is fed to the modulationdemapping, descrambling and soft slicing module 214, which handlesmodulation demapping, descrambling, and soft slicing to prepare thesignal for the rate matching recovery module 216 and turbo decoder 218.The modulation demapping, descrambling and soft slicing module 214 alsoprovides an output to a control channel processing module 228. Layer 2/3processing follows. The processor 200 may further comprise a digitalsignal processor (DSP) 226 used to manage signal flow, hardwareconfiguration, and simple calculations, and control channel processingmachinery.

In one embodiment, the MIMO receiver processing module 202 is furtherconfigured to generate an output that includes a plurality of estimatesof transmit signals transmitted by some or all of the M transmitantennas on some or all of the C channels.

In one embodiment, when M=2 and N=2, the MIMO receiver processing module202 generates the output according to an algorithm expressed as follows:

s(1)=[h*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/D

s*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/D

-   -   where    -   D=|h(1,1)|²+|h(1,2)|²+|h(2,1)|²+|h(2,2)|²

In one embodiment, when M=4 and N=2, the MIMO receiver processing module202 generates the output according to an algorithm expressed as follows:

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)]/D(1)

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)]/D(1)

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)]/D(2)

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)]/D(2)

-   -   where    -   D(1)=|h(1,1)|²+|h(1,3)|²+|h(2,1)|²+|h(2,3)|²    -   D(2)=|h(1,2)|²+|h(1,4)|²+|h(2,2)|²+|h(2,4)|²

In one embodiment, when M=4 and N=4, the MIMO receiver processing module202 generates the output according to an algorithm expressed as follows:

s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)

s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)−h*(3,3)r(3,1)+h(3,1)r*(3,2)−h*(4,3)r(4,1)+h(4,1)r*(4,2)]/D(1)

s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)+h*(3,2)r(3,3)+h(3,4)r*(3,4)+h*(4,2)r(4,3)+h(4,4)r*(4,4)]/D(2)

s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)−h*(3,4)r(3,3)+h(3,2)r*(3,4)−h*(4,4)r(4,3)+h(4,2)r*(4,4)]/D(2)

-   -   where    -   D(1)=|h(1,1)|²+|h(2,1)|²+|h(1,3)|²+|h(2,3)|²+|h(3,1)|²+|h(3,3)|²+|h(4,1)|²+|h(4,3)|²    -   D(2)=|h(1,2)|²+|h(2,2)|²+|h(1,4)|²+|h(2,4)|²+|h(3,2)|²+|h(3,4)|²+|h(4,2)|²+|h(4,4)|²

Exemplary Computing Device

FIG. 300 illustrates a representative computing device 300 that mayimplement the transmit diversity decoding scheme in accordance with anembodiment of the present disclosure. However, it will be readilyappreciated that the techniques disclosed herein may be implemented inother computing devices, systems, and environments. The computing device300 shown in FIG. 3 is only one example of a computing device and is notintended to suggest any limitation as to the scope of use orfunctionality of the computer and network architectures.

In at least one configuration, computing device 300 typically includesat least one processing unit 302 and system memory 304. Depending on theexact configuration and type of computing device, system memory 304 maybe volatile (such as RAM), non-volatile (such as ROM, flash memory,etc.) or some combination thereof. System memory 304 may include anoperating system 306, one or more program modules 308, and may includeprogram data 310.

The computing device 300 is of a very basic configuration demarcated bya dashed line 314. Again, a terminal may have fewer components but mayinteract with a computing device that may have such a basicconfiguration.

In one embodiment, the program module 308 includes a transmit diversitydecoding scheme module 312. The transmit diversity decoding schememodule 312 can carry out one or more functionalities and processes asdescribed above with reference to FIGS. 1-2. For example, when thetransmit diversity decoding scheme module 312 is properly configured,the computing device 300 can carry out the operations of process 100 ofFIG. 1 and variations thereof.

Computing device 300 may have additional features or functionality. Forexample, computing device 300 may also include additional data storagedevices (removable and/or non-removable) such as, for example, magneticdisks, optical disks, or tape. Such additional storage is illustrated inFIG. 3 by removable storage 316 and non-removable storage 318.Computer-readable storage media may include volatile and nonvolatile,removable and non-removable media implemented in any method ortechnology for storage of information, such as computer-executableinstructions, data structures, program modules, or other data. Systemmemory 304, removable storage 316 and non-removable storage 318 are allexamples of computer storage media. Computer-readable storage mediainclude, but are not limited to, RAM, ROM, EEPROM, flash memory or othermemory technology, CD-ROM, digital versatile disks (DVD) or otheroptical storage, magnetic cassettes, magnetic tape, magnetic diskstorage or other magnetic storage devices, or any other medium which canbe used to store the desired information and which can be accessed bycomputing device 300. Any such computer storage media may be part of thecomputing device 300. Computing device 300 may also have input device(s)320 such as keyboard, mouse, pen, voice input device, touch inputdevice, etc. Output device(s) 322 such as a display, speakers, printer,etc. may also be included.

Computing device 300 may also contain communication connections 324 thatallow the device to communicate with other computing devices 326, suchas over a network. These networks may include wired networks as well aswireless networks. Communication connections 324 are some examples ofcommunication media. Communication media may typically be embodied bycomputer readable instructions, data structures, program modules, etc.

It is appreciated that the illustrated computing device 300 is only oneexample of a suitable device and is not intended to suggest anylimitation as to the scope of use or functionality of the variousembodiments described. Other well-known computing devices, systems,environments and/or configurations that may be suitable for use with theembodiments include, but are not limited to personal computers, servercomputers, hand-held or laptop devices, multiprocessor systems,microprocessor-based systems, set top boxes, game consoles, programmableconsumer electronics, network PCs, minicomputers, mainframe computers,distributed computing environments that include any of the above systemsor devices, and/or the like.

CONCLUSION

The above-described techniques pertain to transmit diversity decoding.Although the techniques have been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the appended claims are not necessarily limited to the specificfeatures or acts described. Rather, the specific features and acts aredisclosed as exemplary forms of implementing such techniques. Thoseskilled in the art may make derivations and/or modifications of any ofthe disclosed embodiments or any variations thereof, and suchderivations and modifications are still within the scope of the presentdisclosure.

What is claimed is:
 1. A method, comprising: receiving a first inputthat includes signals transmitted by M transmit antennas on C channelsand received by N receive antennas, M, N and C each being a positiveinteger greater than 1; receiving a second input that includes estimatesof channel matrix elements; and generating an output that includes atleast an estimate of a transmit signal transmitted by one of the Mtransmit antennas on one of the C channels based at least in part on thefirst and the second inputs.
 2. The method as recited in claim 1,wherein generating an output that includes at least an estimate of atransmit signal transmitted by one of the M transmit antennas on one ofthe C channels comprises generating an output that includes a pluralityof estimates of transmit signals transmitted by some or all of the Mtransmit antennas on some or all of the C channels.
 3. The method asrecited in claim 1, wherein, when M=2 and N=2, generating an output thatincludes at least an estimate of a transmit signal transmitted by one ofthe M transmit antennas on one of the C channels comprises generatingthe output according to an algorithm expressed as follows:s(1)=[h*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/Ds*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/Dwherein: D=|h(1,1)|²+|h(1,2)|²+|h(2,1)|²+|h(2,2)|² and wherein:s=detected frequency domain signal; s*=complex conjugate mathematicaloperation of s; r(k,q)=the received signal on carrier (2i+q−1) andreceiver port number (k−1) for 1≦k≦2 and 1≦q≦2; and h(k,q)=the channelpath transmission scaling factor in the frequency domain at carrierfrequencies 2i, 2i+1, 2i+2, and 2i+3 for the port (q−1) transmitter tothe port (k−1) receiver for 1≦k≦2 and 1≦q≦2.
 4. The method as recited inclaim 1, wherein, when M=4 and N=4, generating an output that includesat least an estimate of a transmit signal transmitted by one of the Mtransmit antennas on one of the C channels comprises generating theoutput according to an algorithm expressed as follows:s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)−h*(3,3)r(3,1)+h(3,1)r*(3,2)−h*(4,3)r(4,1)+h(4,1)r*(4,2)]/D(1)s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)+h*(3,2)r(3,3)+h(3,4)r*(3,4)+h*(4,2)r(4,3)+h(4,4)r*(4,4)]/D(2)s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)−h*(3,4)r(3,3)+h(3,2)r*(3,4)−h*(4,4)r(4,3)+h(4,2)r*(4,4)]/D(2)wherein:D(1)=|h(1,1)|²+|h(2,1)|²+|h(1,3)|²+|h(2,3)|²+|h(3,1)|²+|h(3,3)|²+|h(4,1)|²+|h(4,3)|²D(2)=|h(1,2)|²+|h(2,2)|²+|h(1,4)|²+|h(2,4)|²+|h(3,2)|²+|h(3,4)|²+|h(4,2)|²+|h(4,4)|²and wherein: s=detected frequency domain signal; s*=complex conjugatemathematical operation of s; r(k,q)=the received signal on carrier(2i+q−1) and receiver port number (k−1) for 1≦k≦4 and 1≦q≦4; andh(k,q)=the channel path transmission scaling factor in the frequencydomain at carrier frequencies 2i, 2i+1, 2i+2, and 2i+3 for the port(q−1) transmitter to the port (k−1) receiver for 1≦k≦4 and 1≦q≦4.
 5. Aprocessor, comprising: a multiple-input-multiple-output (MIMO) channelestimation module that generates estimates of channel matrix elementswith respect to C channels, C being a positive integer greater than 1;and a MIMO receiver processing module coupled to the MIMO channelestimation module, the MIMO receiver processing module configured to:receive a first input that includes signals transmitted by M transmitantennas on the C channels and received by N receive antennas, M and Neach being a positive integer greater than 1; receive, from the MIMOchannel estimation module, a second input that includes the estimates ofchannel matrix elements with respect to C channels; and generate anoutput that includes at least an estimate of a transmit signaltransmitted by one of the M transmit antennas on one of the C channelsbased at least in part on the first and the second inputs.
 6. Theprocessor as recited in claim 5, wherein the MIMO receiver processingmodule is further configured to generate an output that includes aplurality of estimates of transmit signals transmitted by some or all ofthe M transmit antennas on some or all of the C channels.
 7. Theprocessor as recited in claim 5, wherein, when M=2 and N=2, the MIMOreceiver processing module generates the output according to analgorithm expressed as follows:s(1)=[h*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/Ds*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/Dwherein: D=|h(1,1)|²+|h(1,2)|²+|h(2,1)|²+|h(2,2)|² and wherein:s=detected frequency domain signal; s=complex conjugate mathematicaloperation of s; r(k,q)=the received signal on carrier (2i+q−1) andreceiver port number (k−1) for 1≦k≦2 and 1≦q≦2; and h(k,q)=the channelpath transmission scaling factor in the frequency domain at carrierfrequencies 2i, 2i+1, 2i+2, and 2i+3 for the port (q−1) transmitter tothe port (k−1) receiver for 1≦k≦2 and 1≦q≦2.
 8. The processor as recitedin claim 5, wherein, when M=4 and N=4, the MIMO receiver processingmodule generates the output according to an algorithm expressed asfollows:s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)−h*(3,3)r(3,1)+h(3,1)r*(3,2)−h*(4,3)r(4,1)+h(4,1)r*(4,2)]/D(1)s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)+h*(3,2)r(3,3)+h(3,4)r*(3,4)+h*(4,2)r(4,3)+h(4,4)r*(4,4)]/D(2)s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)−h*(3,4)r(3,3)+h(3,2)r*(3,4)−h*(4,4)r(4,3)+h(4,2)r*(4,4)]/D(2)wherein:D(1)=|h(1,1)|²+|h(2,1)|²+|h(1,3)|²+|h(2,3)|²+|h(3,1)|²+|h(3,3)|²+|h(4,1)|²+|h(4,3)|²D(2)=|h(1,2)|²+|h(2,2)|²+|h(1,4)|²+|h(2,4)|²+|h(3,2)|²+|h(3,4)|²+|h(4,2)|²+|h(4,4)|²and wherein: s=detected frequency domain signal; s*=complex conjugatemathematical operation of s; r(k,q)=the received signal on carrier(2i+q−1) and receiver port number (k−1) for 1≦k≦4 and 1≦q≦4; andh(k,q)=the channel path transmission scaling factor in the frequencydomain at carrier frequencies 2i, 2i+1, 2i+2, and 2i+3 for the port(q−1) transmitter to the port (k−1) receiver for 1≦k≦4 and 1≦q≦4.
 9. Anon-transitory computer-readable medium having a set ofcomputer-executable instructions stored thereon that, when executed byone or more processors, cause the one or more processors to performoperations comprising: receiving a first input that includes signalstransmitted by M transmit antennas on C channels and received by Nreceive antennas, M, N and C each being a positive integer greater than1; receiving a second input that includes estimates of channel matrixelements; and generating an output that includes at least an estimate ofa transmit signal transmitted by one of the M transmit antennas on oneof the C channels based at least in part on the first and the secondinputs.
 10. The non-transitory computer-readable medium as recited inclaim 9, wherein generating an output that includes at least an estimateof a transmit signal transmitted by one of the M transmit antennas onone of the C channels comprises generating an output that includes aplurality of estimates of transmit signals transmitted by some or all ofthe M transmit antennas on some or all of the C channels.
 11. Thenon-transitory computer-readable medium as recited in claim 9, wherein,when M=2 and N=2, generating an output that includes at least anestimate of a transmit signal transmitted by one of the M transmitantennas on one of the C channels comprises generating the outputaccording to an algorithm expressed as follows:s(1)=[h/*(1,1)r(1,1)+h(1,2)r*(1,2)+h*(2,1)r(2,1)+h(2,2)r*(2,2)]/Ds*(2)=[−h*(1,2)r(1,1)+h(1,1)r*(1,2)−h*(2,2)r(2,1)+h(2,1)r*(2,2)]/Dwherein: D=|h(1,1)|²+|h(1,2)|²+|h(2,1)|²+|h(2,2)|² and wherein:s=detected frequency domain signal; s=complex conjugate mathematicaloperation of s; r(k,q)=the received signal on carrier (2i+q−1) andreceiver port number (k−1) for 1≦k≦2 and 1≦q≦2; and h(k,q)=the channelpath transmission scaling factor in the frequency domain at carrierfrequencies 2i, 2i+1, 2i+2, and 2i+3 for the port (q−1) transmitter tothe port (k−1) receiver for 1≦k≦2 and 1≦q≦2.
 12. The non-transitorycomputer-readable medium as recited in claim 9, wherein, when M=4 andN=4, generating an output that includes at least an estimate of atransmit signal transmitted by one of the M transmit antennas on one ofthe C channels comprises generating the output according to an algorithmexpressed as:s(1)=[h*(1,1)r(1,1)+h(1,3)r*(1,2)+h*(2,1)r(2,1)+h(2,3)r*(2,2)+h*(3,1)r(3,1)+h(3,3)r*(3,2)+h*(4,1)r(4,1)+h(4,3)r*(4,2)]/D(1)s*(2)=[−h*(1,3)r(1,1)+h(1,1)r*(1,2)−h*(2,3)r(2,1)+h(2,1)r*(2,2)−h*(3,3)r(3,1)+h(3,1)r*(3,2)−h*(4,3)r(4,1)+h(4,1)r*(4,2)]/D(1)s(3)=[h*(1,2)r(1,3)+h(1,4)r*(1,4)+h*(2,2)r(2,3)+h(2,4)r*(2,4)+h*(3,2)r(3,3)+h(3,4)r*(3,4)+h*(4,2)r(4,3)+h(4,4)r*(4,4)]/D(2)s*(4)=[−h*(1,4)r(1,3)+h(1,2)r*(1,4)−h*(2,4)r(2,3)+h(2,2)r*(2,4)−h*(3,4)r(3,3)+h(3,2)r*(3,4)−h*(4,4)r(4,3)+h(4,2)r*(4,4)]/D(2)wherein:D(1)=|h(1,1)|²+|h(2,1)|²+|h(1,3)|²+|h(2,3)|²+|h(3,1)|²+|h(3,3)|²+|h(4,1)|²+|h(4,3)|²D(2)=|h(1,2)|²+|h(2,2)|²+|h(1,4)|²+|h(2,4)|²+|h(3,2)|²+|h(3,4)|²+|h(4,2)|²+|h(4,4)|²and wherein: s=detected frequency domain signal; s*=complex conjugatemathematical operation of s; r(k,q)=the received signal on carrier(2i+q−1) and receiver port number (k−1) for 1≦k≦4 and 1≦q≦4; andh(k,q)=the channel path transmission scaling factor in the frequencydomain at carrier frequencies 2i, 2i+1, 2i+2, and 2i+3 for the port(q−1) transmitter to the port (k−1) receiver for 1≦k≦4 and 1≦q≦4.